等比數列2條

Since the 5th term is r^3 times the 2nd term, so we have:
8r^3 = 125
r^3 = 125/8
r = 5/2
This yields a geometric progression with common ratio 5/2.

Then the first term is 8/(5/2) = 16/5

To find the 4th term, we use the the the formula ar^(n-1):
(16/5)*(5/2)^(4-1)=50


2. To find the ratio of any two terms, we can divide the 6th term by the 2nd term:

a_6/a_2
=> 4/(1/4) = [r^(6-1)/r^(2-1)]
=> 4/(1/4) = r^(6-2)
=> 16 = r^4
r = 2
Hence the common ratio is 2

b) Then now, solve for the first term:
2nd term = 1st term * common ratio^(2nd term - 1st term)
1/4 = a*(2)^(2-1)
1/4 = a*2
1/8 = a
So, the value of the first term is 1/8.

c) Since the formula for the general term for each geometric progression is a_n = a_1 * r^(n-1)
then substituting a_1 = 1/8, r =2, we have:
a_n = (1/8)*(2)^(n-1)